← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 506 · 40 questions
TalentJR

How to solve it (Same step every time): In an AP the gap (common difference d) is always the same. nth term = a + (n − 1) × d, where a is the first term. Sum of n terms = n × (first + last) ÷ 2; so 1 + 2 + … + n = n × (n + 1) ÷ 2, and the first n odd numbers add up to n × n.

NameDateTime takenScore ___ / 40
  1. 1.Which term of the AP 14, 16, 18, 20, … is 70? (a) 28th (b) 30th (c) 35th (d) 29th
  2. 2.What is the sum of the first 12 terms of the AP 10, 15, 20, …? (a) 900 (b) 450 (c) 480 (d) 65
  3. 3.What is the sum of all the whole numbers from 1 to 49? (a) 1176 (b) 1226 (c) 2450 (d) 1225
  4. 4.What is the sum of the first 8 terms of the AP 10, 12, 14, …? (a) 272 (b) 136 (c) 24 (d) 144
  5. 5.What is the 34th term of the AP 17, 21, 25, 29, …? (a) 136 (b) 149 (c) 132 (d) 153
  6. 6.What is the missing term in the AP 19, 28, ?, 46, 55? (a) 36 (b) 46 (c) 37 (d) 38
  7. 7.Which term of the AP 17, 19, 21, 23, … is 69? (a) 27th (b) 28th (c) 26th (d) 29th
  8. 8.What is the sum of the first 8 terms of the AP 3, 4, 5, …? (a) 56 (b) 10 (c) 52 (d) 104
  9. 9.What is the 12th term of the AP 15, 21, 27, 33, …? (a) 66 (b) 87 (c) 81 (d) 72
  10. 10.What is the 16th term of the AP 12, 14, 16, 18, …? (a) 32 (b) 44 (c) 30 (d) 42
  11. 11.What is the missing term in the AP 9, 12, ?, 18, 21? (a) 14 (b) 16 (c) 18 (d) 15
  12. 12.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 50 (b) 30 (c) 25 (d) 9
  13. 13.What is the sum of the first 5 terms of the AP 9, 10, 11, …? (a) 55 (b) 13 (c) 56 (d) 110
  14. 14.What is the sum of the first 10 terms of the AP 3, 8, 13, …? (a) 280 (b) 48 (c) 255 (d) 510
  15. 15.What is the sum of the first 12 terms of the AP 8, 12, 16, …? (a) 360 (b) 384 (c) 52 (d) 720
  16. 16.What is the sum of the first 5 terms of the AP 4, 6, 8, …? (a) 40 (b) 80 (c) 12 (d) 45
  17. 17.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 43 (c) 484 (d) 506
  18. 18.Which term of the AP 4, 8, 12, 16, … is 148? (a) 36th (b) 39th (c) 38th (d) 37th
  19. 19.What is the 10th term of the AP 20, 27, 34, 41, …? (a) 63 (b) 83 (c) 70 (d) 90
  20. 20.What is the sum of the first 12 terms of the AP 4, 6, 8, …? (a) 180 (b) 192 (c) 26 (d) 360
  21. 21.What is the 27th term of the AP 11, 20, 29, 38, …? (a) 245 (b) 243 (c) 254 (d) 234
  22. 22.What is the 36th term of the AP 20, 29, 38, 47, …? (a) 344 (b) 324 (c) 335 (d) 315
  23. 23.What is the sum of all the whole numbers from 1 to 99? (a) 9900 (b) 4851 (c) 4951 (d) 4950
  24. 24.What is the sum of all the whole numbers from 1 to 65? (a) 2080 (b) 2146 (c) 4290 (d) 2145
  25. 25.What is the sum of all the whole numbers from 1 to 56? (a) 1540 (b) 1568 (c) 3192 (d) 1596
  26. 26.Which term of the AP 8, 14, 20, 26, … is 146? (a) 23rd (b) 24th (c) 25th (d) 26th
  27. 27.What is the sum of the first 9 terms of the AP 6, 8, 10, …? (a) 252 (b) 135 (c) 126 (d) 22
  28. 28.What is the sum of the first 10 terms of the AP 4, 7, 10, …? (a) 31 (b) 350 (c) 175 (d) 190
  29. 29.What is the sum of the first 6 terms of the AP 1, 5, 9, …? (a) 78 (b) 66 (c) 21 (d) 132
  30. 30.What is the missing term in the AP 7, ?, 17, 22, 27? (a) 13 (b) 12 (c) 17 (d) 11
  31. 31.What is the sum of all the whole numbers from 1 to 57? (a) 1653 (b) 1654 (c) 3306 (d) 1596
  32. 32.What is the sum of the first 10 terms of the AP 9, 14, 19, …? (a) 54 (b) 340 (c) 630 (d) 315
  33. 33.What is the 10th term of the AP 19, 28, 37, 46, …? (a) 100 (b) 109 (c) 81 (d) 90
  34. 34.What is the missing term in the AP 1, ?, 15, 22, 29? (a) 7 (b) 15 (c) 9 (d) 8
  35. 35.What is the 24th term of the AP 14, 20, 26, 32, …? (a) 138 (b) 144 (c) 158 (d) 152
  36. 36.What is the 23rd term of the AP 12, 18, 24, 30, …? (a) 150 (b) 132 (c) 138 (d) 144
  37. 37.What is the sum of the first 7 terms of the AP 8, 11, 14, …? (a) 238 (b) 119 (c) 122 (d) 26
  38. 38.What is the 12th term of the AP 15, 17, 19, 21, …? (a) 24 (b) 37 (c) 22 (d) 39
  39. 39.What is the sum of the first 11 terms of the AP 1, 5, 9, …? (a) 231 (b) 462 (c) 253 (d) 41
  40. 40.What is the missing term in the AP 9, 11, 13, ?, 17? (a) 15 (b) 14 (c) 17 (d) 16

Answer key

  1. 29th
  2. 450
  3. 1225
  4. 136
  5. 149
  6. 37
  7. 27th
  8. 52
  9. 81
  10. 42
  11. 15
  12. 25
  13. 55
  14. 255
  15. 360
  16. 40
  17. 484
  18. 37th
  19. 83
  20. 180
  21. 245
  22. 335
  23. 4950
  24. 2145
  25. 1596
  26. 24th
  27. 126
  28. 175
  29. 66
  30. 12
  31. 1653
  32. 315
  33. 100
  34. 8
  35. 152
  36. 144
  37. 119
  38. 37
  39. 231
  40. 15

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad